Quantum Lyapunov control was developed in order to transform a quantum system
from arbitrary initial states to a target state. The idea is to find control
fields that steer the Lyapunov function to zero as $t\rightarrow \infty$,
meanwhile the quantum system is driven to the target state. In order to shorten
the time required to reach the target state, we propose two designs to optimize
Lyapunov control in this paper. The first design makes the Lyapunov function
decrease as fast as possible with a constraint on the total power of control
fields, and the second design has the same purpose but with a constraint on
each control field. Examples of a three-level system demonstrate that the
evolution time for Lyapunov control can be significantly shortened, especially
when high control fidelity is required. Besides, this optimal Lyapunov-based
quantum control is robust against uncertainties in the free Hamiltonian and
decoherence in the system compared to conventional Lyapunov control.Comment: 7 paages, 6 figure
Identifying non-Markovianity with non-divisibility, we propose a measure for non-Markovinity of quantum process. Three examples are presented to illustrate the non-Markovianity, measure for nonMarkovianity is calculated and discussed. Comparison with other measures of non-Markovianity is made. Our non-Markovianity measure has the merit that no optimization procedure is required and it is finite for any quantum process, which greatly enhances the practical relevance of the proposed measure.
We study the quantum-jump-based feedback control on the entanglement shared between two qubits with one of them subject to decoherence, while the other qubit is under the control. This situation is very relevant to a quantum system consisting of nuclear and electron spins in solid states. The possibility to prolong the coherence time of the dissipative qubit is also explored. Numerical simulations show that the quantum-jump-based feedback control can improve the entanglement between the qubits and prolong the coherence time for the qubit subject directly to decoherence.
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